Math 5th Grade Unit - Santa Ana Unified School District

129 Pages·2012·5.4 MB·English

by  Nita Walker

Getting
 to
 the
 Core

  Grade
 5
 Unit
 of
 Study

 Multiplication
 and
 Division
 of
 Fractions

  1
th
Table
 of
 Contents
 5
 Grade
 Math

 Multiplication
 &
 Division
 of
 Fractions

Pages

 Lessons
 and
 Activities

3–8
  Unit
 Overview

9–11
  Prerequisite
 Skills
 Test

12–16
  Preparing
 the
 Learner
 Lesson
 A:

 Preparing
 a
 Fraction
 Bar
 Toolkit

17–21
  Preparing
 the
 Learner
 Lesson
 B:

 Launching
 Mathematical
 Discourse

22–26
  Preparing
 the
 Learner
 Lesson
 C:
 Learning
 the
 Language
 of
 Contrast

27–31
  Lesson
 1:

 Quotients
 of
 Whole
 Numbers

32–41
  Lesson
 2:

 Multiplying
 Whole
 Numbers
 and
 Fractions

42–49
  Lesson
 3:

 Multiplying
 Fractions
 with
 Whole
 Numbers

50–58
  Lesson
 4:

 Multiplying
 Fractions
 with
 Fractions

59–65
  Lesson
 5:

 Multiplying
 Fractions
 by
 Fractions

66–76
  Lesson
 6:

 Comparing
 Size
 of
 Products

77–86
  Lesson
 7:

 Multiplying
 Fractions
 with
 Whole
 Numbers
 and
 Fractions

87–93
  Lesson
 8:

 Division
 of
 Fractions

94–101
  Lesson
 9:

 Dividing
 Unit
 Fractions
 by
 Whole
 Numbers

102–108
  Lesson
 10:

 Dividing
 Unit
 Fractions
 by
 Whole
 Numbers
 and
 Whole

Numbers
 by
 Unit
 Fractions

109–114
  Lesson
 11:

 Dividing
 Unit
 Fractions
 by
 Whole
 Numbers

115–124
  Lesson
 12:
 Culminating
 Task
 and
 Unit
 Assessment

118–122
  Multiple
 Choice
 Test
 with
 Answer
 Key

123–124
  Performance-­‐Based
 Task
 with
 Rubric

125–129
  Additional
 Menu
 Activities
 and
 Check
 Off
 Sheets

  2
on of n
  ntion 3

divisi vatio terve
nd nno on on d in
mmon Core Unit Planner-Mathematics Time Frame: 3 weeks n of whole numbers apply also to the multiplication a actional sides be represented? multiplication of a fraction by a whole number? by a mixed number affect the size of the product? d mixed numbers be used in real life situations? n real life situations? Communication & Collaboration Creativity & I Software Hardware Tier III: Multiply Unit fraction Divide Improper fractiSimplest form Mixed number Mixed number Equivalent fractiDenominator Reciprocal Numerator How will pre-assessment guide instruction? Students missing two or more in any section will neethrough the Preparing the Learner lessons.

  Santa Ana Unified School District Co Multiplying and Dividing Fractions th5 Grade The properties of multiplication and divisiofractions. How are fractions related to division? • How can the area of a rectangle with fr• How can a visual model help to show • How does multiplying by a fraction or • How can multiplication of fractions an• How can division of fractions be used i• Learning and Innovation: Critical Thinking & Problem Solving Information, Media and Technology: Online Tools
 Tier II: Contrast However Although Nevertheless Moreover In addition Similarly nt will be given? est
Unit Title: Grade Level: Big Idea (Enduring nderstandings): Essential Questions: st21 Century Skills: Essential Academic Language: hat pre-assessmeerequisite Skills T

U Wr
P
ksaT
 ecnamrofreP
4

: ng
 experiences
 to
 drive
 responsive
 teaching?)
  Preparing
 the
 Learner
 Lesson
 C
 e
 Learning
 the
 Language
 of
 Contrast
  CCS
 5.4.b
 Multiply
 fractions
 by
 whole
 numbers
 and
 by
 other
 fractions:
 Find
 the
 area
 of
 a
 rectangle
 with
 fractional
 side
 lengths
 by
 tiling
 it
 with
 unit
 squares
 of
 the
 appropriate
 unit
 fraction
 side
 lengths,
 and
 show
 that
 the
 area
 is
 the
 same
 as
 would
 be
 found
 by
 multiplying
 the
 side
 lengths.
 Multiply
 fractional
 side
 lengths
 to
 find
 areas
 of
 rectangles,
 and
 represent
 fraction
 products
 as
 rectangular
 areas.

 The
 area
 of
 a
 rectangle
 with
 fractional
 lengths
 can
 be
 found
 by
 multiplying
 the
 length
 times
 the
 width,
 just
 as
 with
 whole
 numbers.

  CCS5
 .7.a,b,c
 Real
 world
 problems
 with
 division
  of
 fractions
 and

 whole
 numbers:
  Apply
 and
 extend
 previous
 understandings
 of
 division
 to
 divide
 unit
 fractions
 by
 whole
 numbers
 and
 whole
 numbers
 by
 unit
 fractions:
 Interpret
 division
 of
 a
 unit
 fraction
 by
 a
 non-­‐zero
 whole
 number,
 and
 compute
 such
 quotients.

 Interpret
 division
 of
 a
 whole
 number
 by
 a
 unit
 fraction,
 and
 compute
 such
 quotients.
 Division
 of
 fractions
 is
 used
 to
 solve
 problems
 in
 daily
 life.

Instructional Activities s
 engage
 in?
 How
 will
 you
 use
 these
 learni Preparing
 the
 Learner
 Lesson
 B
 Launching
 Mathematical
 Discours CCS
 5.4.a
 Multiply
 fractions
 by
 whole
 numbers
 and
 by
 other
 fractions:
 Apply
 and
 extend
 previous
 understandings
 of
 multiplication
 to
 multiply
 a
 fraction
 or
 whole
 number
 by
 a
 fraction.
 When
 multiplying
 a
 fraction
 times
 a
 whole,
 the
 parts
 of
 the
 fraction
 are
 partitioned
 among
 the
 whole
 number.

  CCS
 5.
 6

 Real
 world
 problems
 APeswith
 multiplication
 of
 fractions
 srfeosand

 mixed
 numbers:
 rsmmVisual
 and
 numeric
 models
 of
 aennctmultiplication
 of
 fractions
 and
 e
 o
 Trmixed
 numbers
 are
 used
 to

 a
 sksolve
 problems
 in
 daily
 life.

t
n
e
What
 learning
 experiences
 will
 stud Preparing
 the
 Learner
 Lesson
 A
 Preparing
 a
 Fraction
 Bar
 Toolkit

 CCS
 5.3
 Interpret
 Fractions
 as

 Division:
 Fractions
 are
 defined
 as
 division
 of
 the
 numerator
 by
 the
 denominator.

  CCS
 5.5.a,b
 Scaling:
 Comparing
 the
 size
 of
 a
 product
 to
 the
 size
 of
 one
 factor
 on
 the
 basis
 of
 the
 size
 of
 the
 other
 factor,
 without
 performing
 the
 indicated
 multiplication.
 Multiplying
 by
 a
 fraction
 reduces
 the
 size
 of
 the
 product,
 while
 multiplying
 by
 a
 mixed
 number
 increases
 the
 size
 of
 the
 product.

(
What does the assessment tell us?
  Ongoing evidence of students’ understanding of the concepts presented Diagnostic information for intervention or acceleration
 Student comprehension of unit concepts and the big idea: The properties of multiplication and division of whole numbers apply also to the multiplication and division of fractions.
  5

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Assessmehat assessments will be utiliit? (F = formative, S = sum Problem solving journal Visual representation of thinkinPerformance Task : Lesson 1-4 Lesson 7 Performance Task Performance Task: CulminatinEnd of Unit Assessment Benchmark Tests her Evidence:
 acher observations
Wun F: F: F: F: S: S: S: OtTe

Standards Common Core Learning Standards Taught and Assessed Common Core Mathematics Content Standards: Number and Operations–Fractions Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 3. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions, mixed numbers, e.g., by using visual fraction models or equations to represent the problem. 4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15.(In general, (a/b) × (c/d) = ac/bd.) b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. 5. Interpret multiplication as scaling (resizing), by: a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n b) to the effect of multiplying a/b by 1. 6. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. 7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship
Do students use the appropriate academic language when speaking in class discussions and presentations and when writing in their daily math journals?
 When talking about mathematics in pairs and groups, do students follow protocol/rules/ routines for collaborative discussions? Can students plan and deliver an informative presentation with appropriately detailed sequencing? Do all students participate in the thinking, conversation, and final product? Do they follow rules and 6

 F: Teacher evaluation of student use of appropriate mathematical academic language
 during partner, small group, and class discussions. S: Use of accurate mathematical terms and appropriate relationship language in culminating
 written word problem and its solution.
 Teacher Evaluation of student speaking and listening: F: Ask and answer questions in pairs and small groups during and after lessons. F: Work collaboratively to solve complex problems while treating each other with respect. F: Participation in presentations of solutions for group work. S: Design and write a recipe using fractional parts which must be multiplied or divided to change the
 quantity of the recipe.
between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Bundled Language Standard(s): 3. Use knowledge of language and its conventions when writing, speaking, reading, or listening. 6. Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal contrast, addition, and other logical relationships (e.g., however, although,
 nevertheless, similarly, moreover, in addition). Bundled Speaking and Listening Standard(s): 1. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. a. Come to discussions prepared having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. b. Follow agreed-upon rules for discussions and carry out assigned roles. c. Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. d. Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. 4. Report on a topic or text, or present an opinion, sequencing ideas logically and using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace.
guidelines for collaboration? Opportunities for Observable Data (How will students demonstrate these Mathematical Practices?) 1. Students analyze fractional parts and understand how they are related to multiplication and division. g 4. Students will create visual models of operations with fractions. 8. Students will notice that Multiplication Properties apply to the multiplication of fractions and mixed numbers. er, colored water-based markers, colored pencils cepts L1; Fractions Multiplication, Fraction Division; NCTM s games: Drop Zone, Fraction Feud, Dig It, Equivalent Fractions, ons made in this unit of study (i.e. literature, science, social ng fractional parts. 7

n pnn i i
(Check all that apply) 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoniof others. 4. Model with mathematics.
  5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Mathematical Tools: tiles or counters, fraction bars, graph paMedia/Technology: ST Math Fraction Concepts; Fraction CoIlluminations Website <http //illuminations.nctm.org> (FractioFraction Game, Fraction Models) Supplementary Materials: Cite several interdisciplinary or cross-content connectstudies, art, etc.) Art projects using tessellations of geometric figures showData analysis where statistics are related as fractions.
y
Standards of Mathematical Practice: Resources/ Materials: InterdisciplinarConnections:
e
n desired student outcomes, what instructional n will be used to address the needs of students with needs, including gifted and talented? Needs- Use of visual organizers in organizing and evaluating evidence. Explicitly teach key academic vocabulary. Monitor student responses for corrective teaching Use of games ST Math Opportunities for verbal rehearsal of concepts Use of pre-assessment results to accelerate/compact curriculum and instruction for students who demonstratmastery (85% +). 8

Based ovariatiospecial Special • • • • • • GATE- •
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ed on desired student outcomes, what instructional ation will be used to address the needs of English rners by language proficiency level? Use of sentence frames (appropriate for language le•to facilitate academic language and conversations. of visual organizers to assist processing mathematicideas Explicitly teach key academic vocabulary. • Use of manipulatives to facilitate conceptual •understanding Flexible grouping to support language acquisition a•target instruction Use of collaboration to promote socio-cultural learn• Opportunities for verbal rehearsal of concepts •
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5th
 Grade
 Fractions
 Prerequisite
 Skills
 Test

Name
 __________________________________

Write
 each
 fraction
 in
 simplest
 form.

1.

 24/28

 ____________

  2.

 6/16

 _______________
  3.

 3
 18/24

 _______________

Solve.
 Write
 your
 answer
 in
 simplest
 form.

4.

 Jake
 had
 10
 apples.
 He
 ate
 some
 of
 the
 apples.
 He
 has
 6
 apples
 left.
 What
 fraction
 of
 the
 original
 apples
 does
 he
 have

left?

__________________________________

5.

 Juan
 and
 his
 friend
 bought
 77
 pieces
 of
 pizza.
 They
 ate
 55
 pieces.
 What
 fraction
 of
 the
 pizza
 did
 they
 eat?

__________________________________

Write
 as
 a
 fraction
 in
 simplest
 form.

6.

 20
 ÷
 40
 =
 ___________________________

  7.

 15
 ÷
 20
 =
 ______________________________

8.

 Are
 3/8
 and
 9/24
 equivalent
 fractions?

 Why
 or
 why
 not?

_________________________________________________________________________________________________

9.

 What
 is
 2
 ½
 written
 as
 an
 improper
 fraction?

 __________________________________

10.

 What
 is
 25/6
 written
 as
 a
 mixed
 number?

 __________________________________

Solve.
 Write
 your
 answer
 as
 a
 fraction
 in
 simplest
 form
 or
 a
 mixed
 number.

11.

 Mabel
 shared
 some
 apples
 with
 her
 friends.
 She
 handed
 out
 ½
 apple
 to
 each
 of
 15
 friends.
 How
 many
 apples
 did
 she

hand
 out?

SAUSD
 Fifth
 Grade
 Common
 Core
 Math
 Unit-­‐-­‐Multiplication
 &
 Division
 of
 Fractions
  9
__________________________________

Name
 __________________________________

12.
 Jane
 wants
 to
 make
 popcorn
 balls.
 Each
 popcorn
 ball
 requires
 1/3
 of
 a
 bag
 of
 popcorn.
 If
 she
 has
 2
 2/3
 bags
 of

popcorn,
 how
 many
 popcorn
 balls
 can
 she
 make?

__________________________________

13.

 José
 has
 84
 model
 trucks.
 He
 wants
 to
 divide
 them
 into
 4
 sets,
 giving
 three
 sets
 to
 friends
 and
 keeping
 one
 set
 for

himself.
 How
 many
 trucks
 will
 be
 in
 each
 set?

__________________________________

14.

 If
 a
 farmer
 has
 54
 mangos,
 how
 many
 boxes
 can
 he
 fill
 with
 6
 mangos
 in
 each
 box?

__________________________________

15.

 Jenna
 is
 giving
 her
 marble
 collection
 away
 to
 her
 friends.
 She
 wants
 to
 divide
 28
 marbles
 equally
 among
 four
 friends.

She
 is
 planning
 to
 give
 6
 marbles
 to
 each
 friend.
 Has
 she
 figured
 out
 the
 right
 number
 to
 give
 to
 each
 person?
 Why

or
 why
 not?

_________________________________________________________________________________________________

Solve.

16.

 What
 is
 125/125
 in
 simplest
 form?

 __________________________________

17.

 What
 is
 327/1
 in
 simplest
 form?

 __________________________________

18.

 If
 45
 X
 75
 is
 3375,
 what
 is
 3375
 ÷
 45?

 __________________________________

Divide
 the
 numbers
 given.
 Check
 your
 work
 to
 show
 your
 answer
 is
 correct.

19.

 85
 ÷
 5
 =
 ________________________

  20.

 1728
 ÷
 4
 =
 __________________________

SAUSD
 Fifth
 Grade
 Common
 Core
 Math
 Unit-­‐-­‐Multiplication
 &
 Division
 of
 Fractions
  10